Cubic Polynomials – A Simpler Approach

An intuitive way to find the 2nd and 3rd roots

While we are all familiar with finding the roots of a quadratic using the Quadratic Equation, it can be complex to find the roots of a higher order polynomial.

We typically need to find one factor by brute force, then divide through to create a quadratic.

I’ve been working on a simpler approach that I’m sharing in this post.

My goal is to make the process a lot simpler by eliminating polynomial long division.

This approach assumes knowledge of algebra and introductory calculus (differentiating polynomials) at the high school level.

I hope it helps you to think in a fresh way about cubic polynomials, and how they can be simpler than first meets the eye!

The method I’ve worked on simply incorporates the known factor into a modified version of the Quadratic Equation, thereby eliminating the division process.

This is the result:

I’ve worked on two methods.

1st Method

The first method is the simpler of the two. It involves writing the polynomial coefficients in factor notation, deriving a Quadratic Equation in terms of the known factor, which can then be solved using a modified version of the standard quadratic formula.

Given y=Ax³+Bx²+Cx+D